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A couple of days ago I posed a question about playing various stack sizes in a series of winner-take-all 6-max tournaments. Basically, you had $10,000 in tournament chips, and you could choose to use them to buy in once for $10,000, five ...
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Ed> “…to figure out whether twenty $500 buy-ins or one hundred $100 buy-ins is superior, determine how often a $100 buy-in will turn into the equivalent of a $500 buy-in. If you have a better than 20% chance to turn a $100 buy-in into the equivalent of a $500 buy-in, then clearly the $100 buy-in is better.”
Ed are you considering that by the time you manage to build your $100 up to $500 and then up to $2000, the stack sizes of the other players will change. You won’t be facing uniform $10,000 stacks any more. Some players will also be short-stacked, and you won’t have any short stack advantage vs. them. Others will have huge stacks and might just call any raise you make hoping to draw out on you. I’m not sure what the overall effect of this is, but it must make things a little more difficult…
Todd,
You are correct that Ed’s conclusions assume that there is not perfect collusion. However, in a winner take all tournament or a cash game, there is little incentive for the big stacks to check down the entire hand, especially when the all-in player is only in for the big blind. But you also have dead small blind and/or big blind money if someone came in with a raise.
JJS,
Here is where we can apply the Independent Chip Model. If we have $2,000 in chips in a winner-take-all tournament, it makes on significant difference to our odds of winning if the other 5 stacks are at $10,000 or if 4 stacks are at $3,000 and one stack is at $38,000.
Isn’t it a problem that we have to start 1/3 of our tourneys out of one of the blinds? In these cases we will have to bet our chip with the very first hand we get dealt.
Klaus,
That’s not an issue. You have to start 1/3 of every tournament out of the blinds, no matter your starting stack. In fact, it’s often to your advantage when you’re in the small blind with 1 big blind rather than 5 or 10. When you have only one, you can complete your blind with impunity and often “save” a portion of your blind equity that way. When you have more money, you’re often forced to simply fold away your blind equity in a similar situation.
Think of it this way. Say on your very first tournament, you draw the big blind. You bet your chip, someone raises, everyone folds to you, and you find out that you’re getting somewhat the worst of it preflop. You lose.
Your total equity has dropped from 100% to 99% of the original. Now think about what happens to your equity if you had bought in for $10,000. You post your blind the first hand, someone raises, and you fold. First off, you don’t get the chance to draw out. Second off, you’re still down to 99% of your original equity. It’s equivalent.
Thanks Ed,
now I see that’s not a problem but I still think that there should be one. It’s because of another poker authority. I’m just reading Harrington’s and Robertie’s book on no limit tournaments. In their chapter ‘Inflection points’ they say that once your stack is smaller than the pot you’re as good as dead. True, they are speaking about the end phase of a tournament but I really doubt that you are better of with that small a stack at the beginning of a tournament. Sure you have a longer time to build a stack but you can drop out any moment. Maybe it’s a mistake to assume that for instance with half a stack you have half the chances to win the tournament compared to a full stack. Couldn’t it be that the chances drop much quicker than the stack gets smaller. This English isn’t good but you sure get what I mean.
I do not doubt that short stacks have an advantage in cash games. Thanks to your efforts I’m quite convinced of that.
What would make a winner-take-all tournament different from a cash game in this instance? If you like, pretend they’re playing with actual black casino $100 chips instead of the fake tournament chips, and whoever happens to end up with all the chips at the end takes them home.
To answer your question about chances dropping more quickly the shorter your stack… why would they? What effect would cause that to happen?
One point, however. Say you’re playing a standard tournament with a regular prize structure. And say your opponents fold to 5-10BB all-ins way too often. You might be better off starting with the 5BB stack rather than starting with a 1BB stack five times. To make it simple, say it’s a SNG and there are four players left. With the 5BB stack you might expect to get around 2nd place. With the 1BB stacks you might expect to get 4th place most of the time and occasionally 1st place (and occasionally 2nd and 3rd too obviously). If you get 2nd place, you win $30. If you win 1st, you get $50. So by starting with the short stacks, you expect roughly 1/5 of $50 or $10, whereas with the 5BB stack you expect somewhere around $30.
Klaus,
I think you have a good point if we have only one or a few chances to get out of being short-stacked. However, we are talking about 100 chances. Your stack size has zero effect on whether any given hand holds up going to the river. Also, we are not basing this on going all-in with a random hand (except for the times you start in the blinds). You can be somewhat selective with the hands you play.
I think you only need to get to 3,000 (30 BB) to get to a comfortable stack size before the first blind increase. At that point, you have some room to play post-flop and you also have a decent amount of fold equity, even against a $10,000 stack. I know your odds aren’t good with one shot, but here you are getting 100 shots at it.
Actually, I’m not sure what I just said is right. You might still rather five shots with 1BB in the SNG described above because you’re still better than 20% to produce a 5BB stack after a couple of hands. I think I tricked myself a little bit when I oversimplified the problem.
CJDCR,
I guess to build a stack of 30 BB starting with 1 BB are something like 1:50 and then we are still a significant dog to win the tournament. We’re only alive. IMO the problem with very short stacks is that we have to win several hands in a row and on average we can expect to double up per won hand and our chances for every single hand are something like 50%. But it may well be that I miss something.
Some 20 years ago I suffered from a similar problem in a backgammon tourney. As avid cash player I gave someone the cube (4) because I figured to be a 75% favourite to win that game. My opponent doubled to 8 and made that game the deciding one. He was right in doing so because he would have had to win 3 games in a row had he passed. The odds against that are 1:7 (1/2*2*2) because his checker play was not superior to mine.
Am I comparing apples with pears here?
Tounces,
Thanks for the note. You make very good points.
…snip…
You are correct that Ed’s conclusions assume that there is not perfect collusion. However, in a winner take all tournament or a cash game, there is little incentive for the big stacks to check down the entire hand, especially when the all-in player is only in for the big blind. But you also have dead small blind and/or big blind money if someone came in with a raise.
…snip…
Let me be clear, I do think there is value in this situation because the bigger stacks have to play against each other and protect the equity in their hands. This is very real and very valuable. It is a little different from a cash game unless it is a freeze out, though. In a cash game, you can take your profit or loss and leave at any time. There is no incentive to get rid of the shorty except to free up a seat for a bigger stack. In this winner take all structure, there is some incentive to knock out a player. This is similar to the effect you see in satellites where every winner wins the same prize. So, I do think collusion is real effect that will mitigate the benefits of the 1BB stack in this structure. It certainly won’t nullify the whole effect.
Toonces>”JJS, Here is where we can apply the Independent Chip Model. If we have $2,000 in chips in a winner-take-all tournament, it makes [no] significant difference to our odds of winning if the other 5 stacks are at $10,000 or if 4 stacks are at $3,000 and one stack is at $38,000.
Well, if we apply ICM then we get the result that I quoted in the other thread, namely, that buying in 100 times for $100 dollars gives you no real advantage over buying in 5 times for $2,000 (advantage is only 0.3% as I calculated there).
However Ed is claiming that the 100 buy-ins is a significant advantage over the 5 buy-ins. Therefore he must not be using ICM.
You can’t have it both ways. Either ICM applies, or it doesn’t.
Intuitively, I have the feeling that the ICM result is correct. But Ed’s answer is different, which leads me to try to find some weak point in it. That was my motivation for my question above.
I am not sure about your statistic on getting from 1 to 30 BBs. Is that assuming 5 races? If so, you probably wouldn’t need to win 5 if your first win or two had multiple opponents as is very probable. Also, you can be more selective so that an individual hand is better than 50%. The greater your stack, the more selective you can be. As for the backgammon comparison, I have never played, so I do not know if it applies. What I do know is that you do not have to necessarily have a superior game to get to 30 BB if you know what hands to push. What you do after that is another story. Even outchipped by others, 30 BB is a good start.
…snip…
You limp, someone raises, and the blinds fold back to you. Or someone raises, you call with your 1 big blind, and everyone folds to the raiser. In either case, you’re risking 1 big blind for the chance to win 2.5 big blinds. You’re getting 5-to-2 on your money. Those are tremendous preflop odds, as you have to win only 29% of the time to turn a profit. On average you should do much better than that. So the very simple scenario of playing heads-up against a open-raiser is, on average, quite profitable.
…snip…
While I agree completely with you’re notion of the 100 buy-ins being best, I do think that you are overstating the value here a bit.
In a winner take all tournament, the rest of the players are strongly incented to work together against you. I think it would be pretty unlikely that a play would bet someone else off a pot you’re in without a huge edge at the time of the bet. So, while you certainly have an advantage of choice, the stack size dynamics probably wouldn’t come into play quite as you described and when they did, you would probably find yourself at a significant disadvantage.